cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A073280 Self-inverse permutation of natural numbers induced by the composition of the Catalan bijections A069770 & A057163.

Original entry on oeis.org

0, 1, 2, 3, 5, 4, 6, 8, 7, 13, 12, 11, 10, 9, 15, 14, 19, 22, 21, 16, 20, 18, 17, 36, 35, 34, 32, 31, 33, 30, 29, 27, 26, 28, 25, 24, 23, 41, 40, 39, 38, 37, 52, 51, 60, 64, 63, 56, 62, 59, 58, 43, 42, 53, 61, 57, 47, 55, 50, 49, 44, 54, 48, 46, 45, 106, 105, 104, 101, 100
Offset: 0

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Links

Crossrefs

Occurs for first time in A073200 as row 9.

Formula

a(n) = A069770(A057163(n)) = A057163(A069770(n)).

A081157 Number of even cycles in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506, with no fixed points of either A057163 or A057164.

Original entry on oeis.org

0, 0, 0, 0, 0, 2, 8, 20, 60, 148, 402, 986, 2474, 5918, 14496, 34708, 84282, 202664, 492048
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Crossrefs

Cf. A014137, A014138, A057505, A057506, A057163, A057164
Bisections: A081158, A081159. Cf. A081150, A081160, A081162.

A080067 a(n) = A057163(A057548(A057164(n))).

Original entry on oeis.org

1, 2, 5, 4, 13, 11, 12, 10, 9, 36, 33, 34, 29, 28, 35, 30, 32, 27, 25, 31, 26, 24, 23, 106, 102, 103, 94, 93, 104, 95, 97, 83, 81, 96, 82, 80, 79, 105, 98, 99, 85, 84, 101, 89, 92, 78, 75, 90, 76, 71, 70, 100, 86, 91, 77, 72, 88, 74, 69, 67, 87, 73, 68, 66, 65, 328, 323, 324
Offset: 0

Views

Author

Antti Karttunen, Jan 27 2003

Keywords

Crossrefs

Iterates starting from zero: A080068. Cf. A080070.

A081162 Number of even cycles in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506, with two fixed-points of A057163.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 15, 0, 56, 0, 185, 0, 655, 0
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Comments

Because A057163 can fix only binary trees of odd size, the even-indexed terms are all 0.

Crossrefs

Bisection: A081163. Cf. A081150, A081157, A081160.
Cf. A014137, A014138, A057505, A057506, A057163.

A082332 Permutation of natural numbers induced by the composition of involutions A069888 & A057163. &F A082332 a(n) = A069888(A057163(n)).

Original entry on oeis.org

0, 1, 2, 3, 6, 4, 8, 5, 7, 19, 16, 11, 14, 9, 22, 21, 13, 15, 10, 18, 20, 12, 17, 60, 56, 47, 53, 44, 33, 30, 39, 51, 42, 25, 28, 37, 23, 64, 63, 59, 62, 58, 36, 35, 41, 52, 43, 27, 29, 38, 24, 50, 49, 55, 61, 57, 32, 34, 40, 26, 46, 48, 54, 31, 45, 191, 186, 172, 182, 168
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082331. Occurs in A073200 as row 576469548397005071. Cf. also A082333-A082334.

A082359 Permutation of natural numbers: composition of permutations A074683 & A057163.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 8, 6, 7, 9, 10, 13, 11, 12, 21, 22, 19, 14, 15, 20, 18, 16, 17, 23, 24, 27, 25, 26, 35, 36, 33, 28, 29, 34, 32, 30, 31, 58, 59, 64, 62, 63, 56, 60, 51, 37, 38, 52, 41, 39, 40, 57, 61, 55, 49, 50, 53, 47, 42, 43, 54, 48, 46, 44, 45, 65, 66, 69, 67, 68
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082360. Occurs in A073200 as row 18764713496857. Cf. also A082357-A082358.

Formula

a(n) = A074683(A057163(n)).

A082360 Permutation of natural numbers: composition of permutations A057163 & A074684.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 8, 6, 9, 10, 12, 13, 11, 17, 18, 21, 22, 20, 16, 19, 14, 15, 23, 24, 26, 27, 25, 31, 32, 35, 36, 34, 30, 33, 28, 29, 45, 46, 49, 50, 48, 58, 59, 63, 64, 62, 57, 61, 54, 55, 44, 47, 56, 60, 53, 42, 51, 37, 38, 43, 52, 40, 41, 39, 65, 66, 68, 69, 67
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082359. Occurs in A073200. Cf. also A082357-A082358.

Formula

a(n) = A057163(A074684(n)).

A085165 A057163-conjugate of A085159.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 6, 8, 9, 12, 16, 17, 21, 10, 18, 11, 14, 15, 13, 19, 20, 22, 23, 26, 30, 31, 35, 42, 43, 44, 45, 49, 56, 57, 58, 63, 24, 32, 47, 46, 59, 25, 48, 28, 37, 38, 29, 39, 40, 41, 27, 50, 33, 51, 52, 34, 53, 54, 55, 36, 60, 61, 62, 64, 65, 68, 72, 73, 77
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

Links

Crossrefs

Inverse: A085166. a(n) = A057163(A085159(A057163(n))) = A085162(A085166(A085162(n))). Occurs in A073200. Cf. also A085162, A086429, A086430.
Number of cycles: A054357. Number of fixed points: A046698. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

A073282 Permutation of natural numbers induced by the composition of the Catalan bijections A072796 & A057163.

Original entry on oeis.org

0, 1, 3, 2, 8, 7, 5, 6, 4, 22, 21, 20, 18, 17, 13, 12, 15, 19, 16, 11, 14, 10, 9, 64, 63, 62, 59, 58, 61, 57, 55, 50, 49, 54, 48, 46, 45, 36, 35, 34, 32, 31, 41, 40, 52, 60, 56, 43, 53, 47, 44, 33, 30, 39, 51, 42, 29, 38, 27, 26, 28, 37, 25, 24, 23, 196, 195, 194, 190, 189
Offset: 0

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Links

Crossrefs

Inverse permutation: A073283. Occurs for first time in A073200 as row 13.

Formula

a(n) = A072796(A057163(n))

A073283 Permutation of natural numbers induced by the composition of the Catalan bijections A057163 & A072796.

Original entry on oeis.org

0, 1, 3, 2, 8, 6, 7, 5, 4, 22, 21, 19, 15, 14, 20, 16, 18, 13, 12, 17, 11, 10, 9, 64, 63, 62, 59, 58, 60, 56, 52, 41, 40, 51, 39, 38, 37, 61, 57, 53, 43, 42, 55, 47, 50, 36, 35, 49, 34, 32, 31, 54, 44, 48, 33, 30, 46, 29, 27, 26, 45, 28, 25, 24, 23, 196, 195, 194, 190, 189
Offset: 0

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Links

Crossrefs

Inverse permutation: A073282. Occurs for first time in A073200 as row 19.

Formula

a(n) = A057163(A072796(n))
Previous Showing 11-20 of 167 results. Next

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